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Decimal expansion of x>0 satisfying 2*x^2-x*cos(x)=4*sin(x).
2

%I #8 Dec 24 2016 18:21:49

%S 1,4,4,0,9,8,5,1,6,3,2,1,0,3,7,3,7,7,8,4,5,1,3,8,0,4,5,4,2,3,4,8,2,8,

%T 4,2,7,0,0,4,4,4,9,0,2,5,8,2,4,3,7,6,1,9,4,5,8,1,2,3,9,0,7,5,8,1,0,0,

%U 9,0,6,8,5,1,7,2,3,1,6,1,3,5,1,8,1,2,2,7,6,6,1,9,1,2,4,3,4,4,9

%N Decimal expansion of x>0 satisfying 2*x^2-x*cos(x)=4*sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%H Matthew House, <a href="/A199739/b199739.txt">Table of n, a(n) for n = 1..10000</a>

%e x=1.44098516321037377845138045423482842700444...

%t a = 2; b = -1; c = 4;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.44, 1.45}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199739 *)

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 10 2011

%E Definition corrected by _Matthew House_, Dec 24 2016